Paracontact metric manifolds without a contact metric counterpart

Abstract

We study non-paraSasakian paracontact metric (κ, μ)-spaces with κ = −1 (equivalent to h2 = 0 but h = 0). These manifolds, which do not have a contact geometry counterpart, will be classified locally in terms of the rank of h. We will also give explicit examples of every possible constant rank of h.